What is the meaning of the straight lines between notes in opposite staves, as shown in the picture? I keep seeing it, but Google and Wikipedia are not helping me.
It means quite simply that the voice in question is moving between the clefs (and usually between the hands as well). In this case, the voice starting with G above middle C falls an octave to be continued in the left hand until it returns to G below middle C, then rises back up an octave to be played in the right hand.
Edit: Here is the original score of this passage (m.10ff of the Ricercar a 6 from the Musical Offering). Looking at the range of the individual voices, you can well imagine the number of times voices will cross between staves when this is transcribed to a Grand Staff.
In Barbershop style notation, such a line indicates that the melody is moving from one voice part to another. By convention, a voice part does not move from one staff to the other.
In this case, it looks as if one musical line (perhaps on a single-note instrument or voice) moves from the treble clef staff to the base clef staff and then back. As a singer, I would find this confusing.